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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.optimization.direct;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.analysis.MultivariateFunction;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.NumberIsTooSmallException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.util.MathUtils;<a name="line.24"></a>
<FONT color="green">025</FONT>    <a name="line.25"></a>
<FONT color="green">026</FONT>    /**<a name="line.26"></a>
<FONT color="green">027</FONT>     * &lt;p&gt;Adapter extending bounded {@link MultivariateFunction} to an unbouded<a name="line.27"></a>
<FONT color="green">028</FONT>     * domain using a penalty function.&lt;/p&gt;<a name="line.28"></a>
<FONT color="green">029</FONT>     *<a name="line.29"></a>
<FONT color="green">030</FONT>     * &lt;p&gt;<a name="line.30"></a>
<FONT color="green">031</FONT>     * This adapter can be used to wrap functions subject to simple bounds on<a name="line.31"></a>
<FONT color="green">032</FONT>     * parameters so they can be used by optimizers that do &lt;em&gt;not&lt;/em&gt; directly<a name="line.32"></a>
<FONT color="green">033</FONT>     * support simple bounds.<a name="line.33"></a>
<FONT color="green">034</FONT>     * &lt;/p&gt;<a name="line.34"></a>
<FONT color="green">035</FONT>     * &lt;p&gt;<a name="line.35"></a>
<FONT color="green">036</FONT>     * The principle is that the user function that will be wrapped will see its<a name="line.36"></a>
<FONT color="green">037</FONT>     * parameters bounded as required, i.e when its {@code value} method is called<a name="line.37"></a>
<FONT color="green">038</FONT>     * with argument array {@code point}, the elements array will fulfill requirement<a name="line.38"></a>
<FONT color="green">039</FONT>     * {@code lower[i] &lt;= point[i] &lt;= upper[i]} for all i. Some of the components<a name="line.39"></a>
<FONT color="green">040</FONT>     * may be unbounded or bounded only on one side if the corresponding bound is<a name="line.40"></a>
<FONT color="green">041</FONT>     * set to an infinite value. The optimizer will not manage the user function by<a name="line.41"></a>
<FONT color="green">042</FONT>     * itself, but it will handle this adapter and it is this adapter that will take<a name="line.42"></a>
<FONT color="green">043</FONT>     * care the bounds are fulfilled. The adapter {@link #value(double[])} method will<a name="line.43"></a>
<FONT color="green">044</FONT>     * be called by the optimizer with unbound parameters, and the adapter will check<a name="line.44"></a>
<FONT color="green">045</FONT>     * if the parameters is within range or not. If it is in range, then the underlying<a name="line.45"></a>
<FONT color="green">046</FONT>     * user function will be called, and if it is not the value of a penalty function<a name="line.46"></a>
<FONT color="green">047</FONT>     * will be returned instead.<a name="line.47"></a>
<FONT color="green">048</FONT>     * &lt;/p&gt;<a name="line.48"></a>
<FONT color="green">049</FONT>     * &lt;p&gt;<a name="line.49"></a>
<FONT color="green">050</FONT>     * This adapter is only a poor man solution to simple bounds optimization constraints<a name="line.50"></a>
<FONT color="green">051</FONT>     * that can be used with simple optimizers like {@link SimplexOptimizer} with {@link<a name="line.51"></a>
<FONT color="green">052</FONT>     * NelderMeadSimplex} or {@link MultiDirectionalSimplex}. A better solution is to use<a name="line.52"></a>
<FONT color="green">053</FONT>     * an optimizer that directly supports simple bounds like {@link CMAESOptimizer} or<a name="line.53"></a>
<FONT color="green">054</FONT>     * {@link BOBYQAOptimizer}. One caveat of this poor man solution is that if start point<a name="line.54"></a>
<FONT color="green">055</FONT>     * or start simplex is completely outside of the allowed range, only the penalty function<a name="line.55"></a>
<FONT color="green">056</FONT>     * is used, and the optimizer may converge without ever entering the range.<a name="line.56"></a>
<FONT color="green">057</FONT>     * &lt;/p&gt;<a name="line.57"></a>
<FONT color="green">058</FONT>     *<a name="line.58"></a>
<FONT color="green">059</FONT>     * @see MultivariateFunctionMappingAdapter<a name="line.59"></a>
<FONT color="green">060</FONT>     *<a name="line.60"></a>
<FONT color="green">061</FONT>     * @version $Id: MultivariateFunctionPenaltyAdapter.java 1422230 2012-12-15 12:11:13Z erans $<a name="line.61"></a>
<FONT color="green">062</FONT>     * @deprecated As of 3.1 (to be removed in 4.0).<a name="line.62"></a>
<FONT color="green">063</FONT>     * @since 3.0<a name="line.63"></a>
<FONT color="green">064</FONT>     */<a name="line.64"></a>
<FONT color="green">065</FONT>    <a name="line.65"></a>
<FONT color="green">066</FONT>    @Deprecated<a name="line.66"></a>
<FONT color="green">067</FONT>    public class MultivariateFunctionPenaltyAdapter implements MultivariateFunction {<a name="line.67"></a>
<FONT color="green">068</FONT>    <a name="line.68"></a>
<FONT color="green">069</FONT>        /** Underlying bounded function. */<a name="line.69"></a>
<FONT color="green">070</FONT>        private final MultivariateFunction bounded;<a name="line.70"></a>
<FONT color="green">071</FONT>    <a name="line.71"></a>
<FONT color="green">072</FONT>        /** Lower bounds. */<a name="line.72"></a>
<FONT color="green">073</FONT>        private final double[] lower;<a name="line.73"></a>
<FONT color="green">074</FONT>    <a name="line.74"></a>
<FONT color="green">075</FONT>        /** Upper bounds. */<a name="line.75"></a>
<FONT color="green">076</FONT>        private final double[] upper;<a name="line.76"></a>
<FONT color="green">077</FONT>    <a name="line.77"></a>
<FONT color="green">078</FONT>        /** Penalty offset. */<a name="line.78"></a>
<FONT color="green">079</FONT>        private final double offset;<a name="line.79"></a>
<FONT color="green">080</FONT>    <a name="line.80"></a>
<FONT color="green">081</FONT>        /** Penalty scales. */<a name="line.81"></a>
<FONT color="green">082</FONT>        private final double[] scale;<a name="line.82"></a>
<FONT color="green">083</FONT>    <a name="line.83"></a>
<FONT color="green">084</FONT>        /** Simple constructor.<a name="line.84"></a>
<FONT color="green">085</FONT>         * &lt;p&gt;<a name="line.85"></a>
<FONT color="green">086</FONT>         * When the optimizer provided points are out of range, the value of the<a name="line.86"></a>
<FONT color="green">087</FONT>         * penalty function will be used instead of the value of the underlying<a name="line.87"></a>
<FONT color="green">088</FONT>         * function. In order for this penalty to be effective in rejecting this<a name="line.88"></a>
<FONT color="green">089</FONT>         * point during the optimization process, the penalty function value should<a name="line.89"></a>
<FONT color="green">090</FONT>         * be defined with care. This value is computed as:<a name="line.90"></a>
<FONT color="green">091</FONT>         * &lt;pre&gt;<a name="line.91"></a>
<FONT color="green">092</FONT>         *   penalty(point) = offset + &amp;sum;&lt;sub&gt;i&lt;/sub&gt;[scale[i] * &amp;radic;|point[i]-boundary[i]|]<a name="line.92"></a>
<FONT color="green">093</FONT>         * &lt;/pre&gt;<a name="line.93"></a>
<FONT color="green">094</FONT>         * where indices i correspond to all the components that violates their boundaries.<a name="line.94"></a>
<FONT color="green">095</FONT>         * &lt;/p&gt;<a name="line.95"></a>
<FONT color="green">096</FONT>         * &lt;p&gt;<a name="line.96"></a>
<FONT color="green">097</FONT>         * So when attempting a function minimization, offset should be larger than<a name="line.97"></a>
<FONT color="green">098</FONT>         * the maximum expected value of the underlying function and scale components<a name="line.98"></a>
<FONT color="green">099</FONT>         * should all be positive. When attempting a function maximization, offset<a name="line.99"></a>
<FONT color="green">100</FONT>         * should be lesser than the minimum expected value of the underlying function<a name="line.100"></a>
<FONT color="green">101</FONT>         * and scale components should all be negative.<a name="line.101"></a>
<FONT color="green">102</FONT>         * minimization, and lesser than the minimum expected value of the underlying<a name="line.102"></a>
<FONT color="green">103</FONT>         * function when attempting maximization.<a name="line.103"></a>
<FONT color="green">104</FONT>         * &lt;/p&gt;<a name="line.104"></a>
<FONT color="green">105</FONT>         * &lt;p&gt;<a name="line.105"></a>
<FONT color="green">106</FONT>         * These choices for the penalty function have two properties. First, all out<a name="line.106"></a>
<FONT color="green">107</FONT>         * of range points will return a function value that is worse than the value<a name="line.107"></a>
<FONT color="green">108</FONT>         * returned by any in range point. Second, the penalty is worse for large<a name="line.108"></a>
<FONT color="green">109</FONT>         * boundaries violation than for small violations, so the optimizer has an hint<a name="line.109"></a>
<FONT color="green">110</FONT>         * about the direction in which it should search for acceptable points.<a name="line.110"></a>
<FONT color="green">111</FONT>         * &lt;/p&gt;<a name="line.111"></a>
<FONT color="green">112</FONT>         * @param bounded bounded function<a name="line.112"></a>
<FONT color="green">113</FONT>         * @param lower lower bounds for each element of the input parameters array<a name="line.113"></a>
<FONT color="green">114</FONT>         * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for<a name="line.114"></a>
<FONT color="green">115</FONT>         * unbounded values)<a name="line.115"></a>
<FONT color="green">116</FONT>         * @param upper upper bounds for each element of the input parameters array<a name="line.116"></a>
<FONT color="green">117</FONT>         * (some elements may be set to {@code Double.POSITIVE_INFINITY} for<a name="line.117"></a>
<FONT color="green">118</FONT>         * unbounded values)<a name="line.118"></a>
<FONT color="green">119</FONT>         * @param offset base offset of the penalty function<a name="line.119"></a>
<FONT color="green">120</FONT>         * @param scale scale of the penalty function<a name="line.120"></a>
<FONT color="green">121</FONT>         * @exception DimensionMismatchException if lower bounds, upper bounds and<a name="line.121"></a>
<FONT color="green">122</FONT>         * scales are not consistent, either according to dimension or to bounadary<a name="line.122"></a>
<FONT color="green">123</FONT>         * values<a name="line.123"></a>
<FONT color="green">124</FONT>         */<a name="line.124"></a>
<FONT color="green">125</FONT>        public MultivariateFunctionPenaltyAdapter(final MultivariateFunction bounded,<a name="line.125"></a>
<FONT color="green">126</FONT>                                                      final double[] lower, final double[] upper,<a name="line.126"></a>
<FONT color="green">127</FONT>                                                      final double offset, final double[] scale) {<a name="line.127"></a>
<FONT color="green">128</FONT>    <a name="line.128"></a>
<FONT color="green">129</FONT>            // safety checks<a name="line.129"></a>
<FONT color="green">130</FONT>            MathUtils.checkNotNull(lower);<a name="line.130"></a>
<FONT color="green">131</FONT>            MathUtils.checkNotNull(upper);<a name="line.131"></a>
<FONT color="green">132</FONT>            MathUtils.checkNotNull(scale);<a name="line.132"></a>
<FONT color="green">133</FONT>            if (lower.length != upper.length) {<a name="line.133"></a>
<FONT color="green">134</FONT>                throw new DimensionMismatchException(lower.length, upper.length);<a name="line.134"></a>
<FONT color="green">135</FONT>            }<a name="line.135"></a>
<FONT color="green">136</FONT>            if (lower.length != scale.length) {<a name="line.136"></a>
<FONT color="green">137</FONT>                throw new DimensionMismatchException(lower.length, scale.length);<a name="line.137"></a>
<FONT color="green">138</FONT>            }<a name="line.138"></a>
<FONT color="green">139</FONT>            for (int i = 0; i &lt; lower.length; ++i) {<a name="line.139"></a>
<FONT color="green">140</FONT>                // note the following test is written in such a way it also fails for NaN<a name="line.140"></a>
<FONT color="green">141</FONT>                if (!(upper[i] &gt;= lower[i])) {<a name="line.141"></a>
<FONT color="green">142</FONT>                    throw new NumberIsTooSmallException(upper[i], lower[i], true);<a name="line.142"></a>
<FONT color="green">143</FONT>                }<a name="line.143"></a>
<FONT color="green">144</FONT>            }<a name="line.144"></a>
<FONT color="green">145</FONT>    <a name="line.145"></a>
<FONT color="green">146</FONT>            this.bounded = bounded;<a name="line.146"></a>
<FONT color="green">147</FONT>            this.lower   = lower.clone();<a name="line.147"></a>
<FONT color="green">148</FONT>            this.upper   = upper.clone();<a name="line.148"></a>
<FONT color="green">149</FONT>            this.offset  = offset;<a name="line.149"></a>
<FONT color="green">150</FONT>            this.scale   = scale.clone();<a name="line.150"></a>
<FONT color="green">151</FONT>    <a name="line.151"></a>
<FONT color="green">152</FONT>        }<a name="line.152"></a>
<FONT color="green">153</FONT>    <a name="line.153"></a>
<FONT color="green">154</FONT>        /** Compute the underlying function value from an unbounded point.<a name="line.154"></a>
<FONT color="green">155</FONT>         * &lt;p&gt;<a name="line.155"></a>
<FONT color="green">156</FONT>         * This method simply returns the value of the underlying function<a name="line.156"></a>
<FONT color="green">157</FONT>         * if the unbounded point already fulfills the bounds, and compute<a name="line.157"></a>
<FONT color="green">158</FONT>         * a replacement value using the offset and scale if bounds are<a name="line.158"></a>
<FONT color="green">159</FONT>         * violated, without calling the function at all.<a name="line.159"></a>
<FONT color="green">160</FONT>         * &lt;/p&gt;<a name="line.160"></a>
<FONT color="green">161</FONT>         * @param point unbounded point<a name="line.161"></a>
<FONT color="green">162</FONT>         * @return either underlying function value or penalty function value<a name="line.162"></a>
<FONT color="green">163</FONT>         */<a name="line.163"></a>
<FONT color="green">164</FONT>        public double value(double[] point) {<a name="line.164"></a>
<FONT color="green">165</FONT>    <a name="line.165"></a>
<FONT color="green">166</FONT>            for (int i = 0; i &lt; scale.length; ++i) {<a name="line.166"></a>
<FONT color="green">167</FONT>                if ((point[i] &lt; lower[i]) || (point[i] &gt; upper[i])) {<a name="line.167"></a>
<FONT color="green">168</FONT>                    // bound violation starting at this component<a name="line.168"></a>
<FONT color="green">169</FONT>                    double sum = 0;<a name="line.169"></a>
<FONT color="green">170</FONT>                    for (int j = i; j &lt; scale.length; ++j) {<a name="line.170"></a>
<FONT color="green">171</FONT>                        final double overshoot;<a name="line.171"></a>
<FONT color="green">172</FONT>                        if (point[j] &lt; lower[j]) {<a name="line.172"></a>
<FONT color="green">173</FONT>                            overshoot = scale[j] * (lower[j] - point[j]);<a name="line.173"></a>
<FONT color="green">174</FONT>                        } else if (point[j] &gt; upper[j]) {<a name="line.174"></a>
<FONT color="green">175</FONT>                            overshoot = scale[j] * (point[j] - upper[j]);<a name="line.175"></a>
<FONT color="green">176</FONT>                        } else {<a name="line.176"></a>
<FONT color="green">177</FONT>                            overshoot = 0;<a name="line.177"></a>
<FONT color="green">178</FONT>                        }<a name="line.178"></a>
<FONT color="green">179</FONT>                        sum += FastMath.sqrt(overshoot);<a name="line.179"></a>
<FONT color="green">180</FONT>                    }<a name="line.180"></a>
<FONT color="green">181</FONT>                    return offset + sum;<a name="line.181"></a>
<FONT color="green">182</FONT>                }<a name="line.182"></a>
<FONT color="green">183</FONT>            }<a name="line.183"></a>
<FONT color="green">184</FONT>    <a name="line.184"></a>
<FONT color="green">185</FONT>            // all boundaries are fulfilled, we are in the expected<a name="line.185"></a>
<FONT color="green">186</FONT>            // domain of the underlying function<a name="line.186"></a>
<FONT color="green">187</FONT>            return bounded.value(point);<a name="line.187"></a>
<FONT color="green">188</FONT>    <a name="line.188"></a>
<FONT color="green">189</FONT>        }<a name="line.189"></a>
<FONT color="green">190</FONT>    <a name="line.190"></a>
<FONT color="green">191</FONT>    }<a name="line.191"></a>




























































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